Metal foams physics

232 Pages·2008·48.939 MB·English

by  CarolinKorner

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for Viktor and Walter

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Preface
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A person with a new idea is a crank until the idea sucOceeds.
Mark Twain
Metal foams show outstanding properties: Low weight, higRh rigidity, high energy
absorption capacity, high damping capacity, etc. They have attracted strong in-
dustrial and scientific interest during the last decade. A variety of methods has
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been developed to produce foams and the development of new, more sophisticated
methods is still going on.
On the one hand, there are only very few applic ations where metal foams can
be directly employed without further processing.DOn the other hand, established
metal foam production methods have one feature in common, they produce foam
and not metal parts containing metal foam. In the majority of cases additional
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shapingandjoiningstepsarenecessarytotransformthemetalfoamintoaworking
functional element. In addition, the cellular structure demands for appropriate
joining technologies which are often not yeTt available or expensive. As a result, the
whole processing sequence is in general long and expensive.
The logical consequence of the requCirement to develop cost-effective techniques
to produce metal parts with integrated cellular structure is the newly developed
process of integral foam molding. Integral foam consists of a solid skin and a cel-
lular core. This is the fundamenEtal construction principle which is ubiquitous in
biologicalsystems,e.g.thehumanskull,aswellasintechnicalsolutions,e.g.sand-
wichconstructions. Theconcentrationofthematerialwithintheskinoptimizesthe
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moment of inertia and thus stiffness and strength.
Thedevelopmentofmetalbasedintegralfoamfollowsanalogouspathsasthatof
polymerswhereintegralfoRamwascommerciallyintroducedinthelate1960s. Poly-
mer integral foam parts are now accepted as a material system with characteristic
propertieswhichsimplifiesdesigns,reducesproductioncostsandweight,andwhich
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increasesstiffnessandoverallstrength. Startingfromlow-pressureinjectionofpoly-
mers with small amounts of gas content, highly sophisticated processes have been
developedwhereinjectiontakesplaceatveryhighpressuresintomoldcavitieswith
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moving elements.
Metal integral foams represent – analogous to polymers – an own class of struc-
tureswithspNecificpropertiessuchashighstructuralrigidity,highenergyabsorption
capacityorhighdamping. Theyarenotthoughttosubstitutestandarddiecastings
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but open new applications and also demand a specific component design. Com-
pared to polymers, the development of metal integral foam molding is just at the
beginning. The time delay of four decades between commercialization oFf polymer
integralfoammoldingandthecurrentonsetofinvestigationswithrespecttometals
canhardlybeexplained. Althoughwehavemadeenormousprogressduringthelast
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years of metal integral foam molding research there are still many challenges left
which have to be solved in the future to get integral foam components made from
light metals into broad industrial application. Nevertheless, weOpresume a large
economical potential for metal integral foam molding technologies in the future.
Surprisingly, integral foam molding of metals shows much more similarities than
differences to polymer integral foam molding. This is not onRly true for the applied
molding technologies but also for the resultant integral foam structures and their
properties. The intention of this book is to introduce the technological principles
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of metal integral foam molding. In addition, its purpose is to reveal the underly-
ing physical mechanisms which govern the foam evolution process and which are
essential in view of a successful process development .
Usually, a first step to gain a physical picture oDf the integral foam molding pro-
cess would be to observe it. Unfortunately, in situ experimental observations are
impossible since the foaming process takes place in a permanent steel mold within
a fraction of a second. Thus, information of tEhe foam formation process has to be
extracted from ex situ investigations. This limited information does not help very
muchtounderstandtheunderlyingphysicTs. Nevertheless,incombinationwiththe-
oreticalinvestigationsandnumericalsimulationtheexperimentalfindingsrevealthe
underlying physical principles.
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The book is organized in three parts:
• Part I: Technology E
PartIdescribesthetechnologicalfoundationofintegralfoammoldingofmet-
als,atechnologythathasbeenconceivedanddevelopedinourresearchgroup
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at the University of Erlangen throughout the last 6 years. For the first time
itisshownthatfoamingofmetalsispossiblebyapplyingmoldingtechniques
very similar to polyRmer integral foam molding. A low pressure and a high
pressure integral foam molding process are introduced and discussed. The
moldedpartsshowcompactskinsandfoamedcoreswithporositiesupto80%.
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Thermodynamicsandkineticsoftheblowingagentaswellasthelowviscosity
of metal melts turn out to be the key for the success of the molding process.
Although non-conditioned metal melts are employed, which are generally be-
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lieved to be not foamable, the resulting structures are in fact foams. Integral
foam molding appears to be the only known process where non-conditioned
metal mNelts may be used to produce foam. An explanation of this finding is
givenonthebasisofthetheoreticalbackgroundpresentedinPartIIandPart
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III. The fact that standard casting alloys may be applied has enormous ad-
vantages with respect to casting behavior, properties, recycling and, last but
not least, costs. F
• Part II: Physics
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Thispartisdevotedtothephysicsoffoamingwithspecialemphasisonthevery
short time scale which is characteristic for integral foam molding. Although
very complex in detail, foam formation is shown to underlieOsimple evolution
lawsdeterminedbythewayhowfoamstabilizationisrealized. Basisforthese
investigations is a numerical approach which is described in Part III. In or-
der to account for the specific situation during integraRl foam molding, foam
evolution in the presence of solid particles is discussed in detail. The results
of these theoretical considerations represent the basis for the interpretation
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of the experimental observations described in Part I. However, the evolution
laws are generally valid and can as well be applied to other foam evolution
processes.
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• Part III: Numerical Simulation
The high degree of complexity of foam evolution processes strongly restricts
analyticaldescriptions. EvenwiththeaidEofnumericaltools,thesimulationof
foamformationprocessesisachallengeduetothehugeandstronglyevolving
gas–liquid interface. A new lattice Boltzmann approach for the treatment of
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free surfaces is developed and applied on foam evolution problems. For the
firsttime,thenumericalsimulationoffoamevolutionstartingfromnucleation
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until decay is accessible. The interplay between hydrodynamics, capillary
forces, gravity and bubble coalescence processes leads to complex phenomena
suchastopologicalrearrangeEments,avalanches,drainage,etc. withoutfurther
model assumptions.
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Even if integral foam molding of light metals will never find general industrial
application,wehavegainedfundamentalinsightsintothemainmechanismsoffoam
evolution, especially into tRhe general principles of metal foam stabilization.
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Acknowledgments
Thisworkisbasedonresultsobtainedduringmyworkastheleaderofthelightweight
materialsgroupattheInstituteofScienceandTechnologyofMetalsattheUniver-
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sity of Erlangen-Nuremberg.
IappreciatethesupportandfreedomIobtainedfromProf. R.F.Singer,thehead
of the InstituNte of Science and Technology of Metals, as it enabled me to follow-up
and realize own ideas.
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IwouldliketothankallmembersoftheInstituteforMaterialsSciencewhocon-
tributedtothisworkinoneoranotherway. Althoughitisimpossibletoacknowledge
all contributors, the work of the following colleagues is especially apprecFiated: M.
Arnold, Dr. M. Hirschmann, Dr. M. Thies, A. Trepper and H. Wiehler.
In addition, I would like to thank Prof. Rüde, Prof. Kaptay, Prof. Greil and
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Prof. Clyne for the support during the habilitation process and the colleagues of
Neue Materialien Fürth GmbH for the assistance with the thixomolder.
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Carolin Körner, April 2008
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Contents
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Preface VII
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I TECHNOLOGY 1
1 Introduction P 5
1.1 Integral Foam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Polymer Integral Foam Molding . . . . . . . . . . . . . . . . . . . . . 13
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2 Integral Foam Molding of Metals 19
2.1 Basic Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Admixing of the Blowing Agent . . .E. . . . . . . . . . . . . . . . . . 24
2.3 Low Pressure Integral Foam Molding . . . . . . . . . . . . . . . . . . 27
2.4 High Pressure Integral Foam Molding . . . . . . . . . . . . . . . . . . 32
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2.5 Base Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.6 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
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3 Structure and Properties 45
3.1 Density Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
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3.2 Foam Structure Evolution . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4 Synopsis . . . . . . .R. . . . . . . . . . . . . . . . . . . . . . . . . . . 71
II PHYSICS R 73
4 Physics of Foaming 77
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4.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2 Bubble Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3 Stabilization Mechanisms. . . . . . . . . . . . . . . . . . . . . . . . . 89
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5 Evolution Laws 103
5.1 FunNdamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.2 Non-stabilized Evolution . . . . . . . . . . . . . . . . . . . . . . . . . 106
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5.3 Stabilized Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.4 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
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6 Endogenous Stabilization 123
6.1 Disjoining Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
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6.2 Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.3 Foam Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.4 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
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III NUMERICAL SIMULATION 139
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7 Theoretical Approach 143
7.1 State-of-the-Art . . . . . . . . . . . . . . . . .P. . . . . . . . . . . . . 144
7.2 Physical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.3 Lattice Boltzmann Approach. . . . . . . . . . . . . . . . . . . . . . . 152

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8 LBM for Free Surface Flow 163
8.1 Free Surface and Fluid Advection . . . . . . . . . . . . . . . . . . . . 164
8.2 Interface Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . 167
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9 LBM for Foam Evolution 171
9.1 Gas Bubbles and Gas Transport T. . . . . . . . . . . . . . . . . . . . . 171
9.2 Interfacial Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
9.3 Foam Formation PhenomenaC. . . . . . . . . . . . . . . . . . . . . . . 177
A Gas Supply and Gas Diffusion 185
A.1 Generalized Johnson-MehEl-Avrami Approach . . . . . . . . . . . . . . 185
A.2 Gas Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
B Miscellany R 189
B.1 Foaming Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
B.2 Mean Cell Diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
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B.3 Curvature Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 193
C Material ParameOters 195
Symbols 199
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Bibliography 203
Index 221
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Part I
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TECHNOLOGY
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